Question: Multiply the following complex numbers: $({1-i}) \cdot ({-3+i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1-i}) \cdot ({-3+i}) = $ $ ({1} \cdot {-3}) + ({1} \cdot {1}i) + ({-1}i \cdot {-3}) + ({-1}i \cdot {1}i) $ Then simplify the terms: $ (-3) + (1i) + (3i) + (-1 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -3 + (1 + 3)i - 1i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -3 + (1 + 3)i - (-1) $ The result is simplified: $ (-3 + 1) + (4i) = -2+4i $